This is how I would do it. (I've never used y to represent 2x, but maybe your teacher does that.)

2sin2x = 1
sin2x = 1/2

If we reference the unit circle (which should be in your head), then we know that sine corresponds to the y-coordinate. y=1/2 happens at 30 and 150 degrees. Since we have "2x," we must make two passes around the unit circle, so add 360 to both of those angles. 30+360 = 390 and 150+360 = 510.